Problem: Simplify to lowest terms. $\dfrac{70}{30}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 70 and 30? $70 = 2\cdot5\cdot7$ $30 = 2\cdot3\cdot5$ $\mbox{GCD}(70, 30) = 2\cdot5 = 10$ $\dfrac{70}{30} = \dfrac{7 \cdot 10}{ 3\cdot 10}$ $\hphantom{\dfrac{70}{30}} = \dfrac{7}{3} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{70}{30}} = \dfrac{7}{3} \cdot 1$ $\hphantom{\dfrac{70}{30}} = \dfrac{7}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{70}{30}= \dfrac{2\cdot35}{2\cdot15}= \dfrac{2\cdot 5\cdot7}{2\cdot 5\cdot3}= \dfrac{7}{3}$